Method and apparatus for acquiring wide-band pseudorandom noise encoded waveforms

ABSTRACT

The method and apparatus of the present invention is directed to architectures for signal processing, such as for performing analog-to-digital and digital-to-analog conversions, in which the source signal is decomposed into subband signals by an analysis filter, processed, and the processed subband signals combined to form a reconstructed signal that is representative of the source signal.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a divisional of U.S. Patent Application Ser.No. 09/137,383, filed Aug. 20, 1998, to Kober et al., which claimspriority under 35 U.S.C. § 119(e) from U.S. Provisional Application Ser.Nos. 60/087,036, filed May 28, 1998; 60/056,455, filed Aug. 21, 1997;and 60/056,228, filed Aug. 21, 1997, all of which are incorporatedherein by this reference.

The U.S. Government has a paid-up license in this invention and theright in limited circumstances to require the patent owner to licenseothers on reasonable terms as provided for by the terms of ContractN00014-98-M-0130 awarded by the Office of Naval Research and ContractNo. F33615-98-C-1316 awarded by the Air Force Research Laboratory.

FIELD OF THE INVENTION

The present invention relates generally to a method and apparatus foracquiring wide-band random and pseudorandom noise encoded waveforms andspecifically to a method and apparatus for acquiring wide-band signals,including deterministic signals, random signals and pseudorandom noiseencoded waveforms that divides the waveform into a plurality of subbandsprior to signal processing thereof.

BACKGROUND

Analog-to-digital converters are devices that convert real world analogsignals into a digital representation or code which a computer canthereafter analyze and manipulate. Analog signals represent informationby means of continuously variable physical quantities while digitalsignals represent information by means of differing discrete physicalproperty states. Converters divide the full range of the analog signalinto a finite number of levels, called quantization levels, and assignsto each level a digital code. The total number of quantization levelsused by the converter is an indication of its fidelity and is measuredin terms of bits. For example, an 8-bit converter uses 2⁸ or 256 levels,while a 16-bit converter uses 2¹⁶ or 65536 levels.

During the conversion process, the converter determines the quantizationlevel that is closest to the amplitude of the analog signal at that timeand outputs the digital code that represents the selected quantizationlevel. The rate at which the output is created indicates the speed ofthe converter and is measured in terms of samples per second (sps) orfrequency in Hertz (Hz). As will be appreciated, a larger number of bitsand therefore quantization levels equates into a finer representation ofthe analog signal.

In designing an analog-to-digital converter, there are a number ofconsiderations. In many applications for example it is desirable thatthe converter has not only a high rate of speed but also a large numberof quantization levels or a high degree of fidelity. Such converters aredifficult to build and therefore tend to be highly complex and veryexpensive. The key reason is that conversion errors and theconsequential device layout constraints for reducing such errors, bothof which can be ignored at slow speeds, can become significant at highspeeds. As a result, in existing converters, high fidelity and highspeed are commonly mutually exclusive; that is, the higher the converterspeed the lower the converter fidelity and vice versa.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an analog-to-digitalconverter that has a high fidelity and a high speed. Related objectivesare to provide such an analog-to-digital converter that is relativelysimple and inexpensive.

The present invention is directed to a method and apparatus forprocessing signals, particularly wide-band signals, includingdeterministic signals, random signals, and signals defined bypseudorandom waveforms with a relatively high degree of fidelity andefficiency at a high speed and at a low cost. The invention isparticularly useful for processing wideband signal, including signalsdefined by broadband signals (i.e., signals having a bandwidth ofpreferably more than about 1 kHz and more preferably more than about 1GHz).

The signal can be in any suitable form such as electromagneticradiation, acoustic, electrical and optical.

In one embodiment, the method includes the following steps:

(a) decomposing the analog or digital signal into a plurality of signalsegments (i.e., subband signals), each signal segment having a signalsegment bandwidth that is less than the signal bandwidth;

(b) processing each of the signal segments to form a plurality ofprocessed signal segments; and

(c) combining the processed signal segments into a composite signal thatis digital when the signal is analog and analog when the signal isdigital. As will be appreciated, the sum of the plurality of signalbandwidths is approximately equivalent to the signal bandwidth. Themeans for processing the signal segments can include any number ofoperations, including filtering, analog-to-digital or digital-to-analogconversion, signal modulation and/or demodulation, object tracking, RAKEprocessing, beam forming, null steering, correlation,interference-suppression and matched subspace filtering.

In a particularly preferred application, the signal processing step (b)includes either analog-to-digital or digital-to-analog conversions. Theuse of signal segments rather than the entire signal for suchconversions permits the use of a lower sampling rate to retainsubstantially all of the information present in the source signal.According to the Bandpass Sampling Theorem, the sampling frequency ofthe source signal should be at least twice the bandwidth of the sourcesignal to maintain a high fidelity. The ability to use a lower samplingfrequency for each of the signal segments while maintaining a highfidelity permits the use of a converter for each signal segment that isoperating at a relatively slow rate. Accordingly, a plurality ofrelatively inexpensive and simple converters operating at relativelyslow rates can be utilized to achieve the same rate of conversion as asingle relatively high speed converter converting the entire signal withlittle, if any, compromise in fidelity.

The means for decomposing the signal into a number of signal segmentsand the means for combining the processed signal segments to form thecomposite signal can include any number of suitable signal decomposingor combining devices (e.g., filters, analog circuitry, computersoftware, digital circuitry and optical filters). Preferably, aplurality or bank of analog or digital analysis filters is used toperform signal decomposition and a plurality or bank of analog ordigital synthesis filters is used to perform signal reconstruction. Theanalysis and synthesis filters can be implemented in any number of waysdepending upon the type of signal to be filtered. Filtration can be by,for example, analog, digital, acoustic, and optical filtering methods.By way of example, the filters can be designed as simple delays or verysophisticated filters with complex amplitude and phase responses.

In a preferred configuration, a plurality or bank of analysis and/orsynthesis filters, preferably designed for perfect reconstruction, isused to process the signal segments. As will be appreciated perfectreconstruction occurs when the composite signal, or output of thesynthesis filter bank, is simply a delayed version of the source signal.

In one configuration, the analysis filters and synthesis filters arerepresented in a special form known as the Polyphase representation. Inthis form, Noble identities are can be used to losslessly move thedecimators to the left of the analysis filters and the interpolators tothe right of the synthesis filters.

In another configuration, noise components in each of the signalsegments can be removed prior to signal analysis or conversion in theprocessing step. The removal of noise prior to analog-to-digitalconversion can provide significant additional reductions incomputational requirements.

In yet another configuration, a coded signal is acquired rapidly usingthe above-referenced invention. In the processing step, the signalsegments are correlated with a corresponding plurality of replicatedsignals to provide a corresponding plurality of correlation functionsdefining a plurality of peaks; an amplitude, time delay, and phase delayare determined for at least a portion of the plurality of peaks; and atleast a portion of the signal defined by the signal segments isrealigned and scaled based on one or more of the amplitude, time delay,and phase delay for each of the plurality of peaks.

In another embodiment, a method is provided for reducing noise in asignal expressed by a random or pseudorandom waveform. The methodincludes the steps of decomposing the signal into a plurality of signalsegments and removing a noise component from each of the signal segmentsto form a corresponding plurality of processed signal segments. Themeans for decomposing the signal can be any of the devices noted above,and the means for removing the noise component includes a noise reducingquantizer, noise filters and rank reduction. Signal reconstruction mayor may not be used to process further the processed signal segments.This embodiment is particularly useful in acquiring analog signals.

In yet a further embodiment, a method is provided for combining aplurality of signal segments (which may or may not be produced byanalysis filters). In the method, synthesis filtering is performed oneach of the plurality of signal segments. The means for performingsynthesis filtering can be any of the devices noted above.

A number of differing system configurations can incorporate thesynthesis filtering means in this embodiment of the invention. Forexample, a system can include, in addition to the synthesis filteringmeans, means for emitting the plurality of signal segments from aplurality of signal sources (e.g., antennas); means for receiving eachof the plurality of signal segments (e.g., antennas); and means forconverting each of the signal segments from analog format to digitalformat (e.g., analog-to-digital converter).

In another configuration, the system includes: a plurality of analysisfilters to decompose a source signal into a plurality of decomposedsignal segments; a plurality of digital-to-analog conversion devices forconverting the plurality of decomposed signal segments from digital intoanalog format to form a corresponding plurality of analog signalsegments; a plurality of amplifiers to form a corresponding plurality ofsignal segments; a plurality of signal emitters for emitting theplurality of signal segments; and a plurality of receptors for receivingthe plurality of signal segments.

In yet another configuration, the system includes: a plurality ofanalysis filters to decompose a source signal into a plurality ofdecomposed signal segments; a plurality of amplifiers to amplify thedecomposed signal segments to form a corresponding plurality of signalsegments; a plurality of signal emitters for emitting the plurality ofsignal segments; and a plurality of receptors for receiving theplurality of signal segments.

In another embodiment, a method is provided in which digital signals aredecomposed, processed, and then recombined. Signal processing caninclude signal correlation (e.g., signal modulation or demodulation),and oblique projection filtration (e.g., as described in copending U.S.patent application Ser. No. 08/916,884 filed Aug. 22, 1997, entitled“RAKE Receiver For Spread Spectrum Signal Demodulation,” which isincorporated herein fully by reference).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a first embodiment of the present invention;

FIG. 2 depicts an analog signal;

FIG. 3 depicts the analog signal of FIG. 2 divided up into a pluralityof signal segments;

FIG. 4 depicts the first embodiment including decimation;

FIGS. 5A and 5B depict noble identities;

FIG. 6 depicts a polyphase filter representation;

FIG. 7 depicts a polyphase filter representation with noble identities;

FIG. 8 depicts another embodiment of the present invention;

FIG. 9 depicts the quantization process of the quantizers in FIG. 8;

FIG. 10 depicts a subband digital transmitter;

FIG. 11 depicts a subband analog transmitter;

FIG. 12 depicts a subband receiver;

FIG. 13 depicts rank reduction for noise filtering;

FIG. 14 depicts another embodiment of the present invention;

FIG. 15 depicts another embodiment of the present invention;

FIG. 16 depicts RAKE processing;

FIG. 17 depicts a multiplexed radar transmitter architecture;

FIG. 18 depicts a radar receiver architecture;

FIG. 19 depicts a digital communications example of a recursive,adaptive Wiener filter;

FIG. 20 depicts an alternative RAKE processing methodology; and

FIG. 21 depicts a least squares, multiple input multiple output filterdesign problem.

DETAILED DESCRIPTION

Referring to FIG. 1, an embodiment of the present invention isillustrated. As can be seen from FIGS. 1 and 2, a wideband, pseudorandomor random signal 40 (shown in FIG. 2) is passed to a bank or pluralityof analysis filters 44 a-n. The signal 40 has a frequency band ordomain, F_(s), having frequency bounds, f₀ (lower) and f_(n) (upper),and therefore a bandwidth of f₀-_(n) (FIG. 2). The bandwidth commonly isat least about 1 kHz, more commonly at least about 1 GHz. Each of theanalysis filters 44 a-n pass only a portion of the frequency band of thesignal to form a plurality of subband signals 48 a-n, or time frequencycomponents, characterized by discrete portions of the frequency band,F_(s), of the signal 40 (FIG. 3). As will be appreciated, the summationof the individual frequency bandwidths of all of the subband signals 48a-n is substantially the same as the bandwidth of the signal 40 (FIG.3). The various subband signals 48 a-n are processed 52 a-nindependently as described below to form a corresponding plurality ofprocessed signal segments 56 a-n. The processed signal segments 56 a-nare passed to a bank or plurality of synthesis filters 60 a-n andcombined to form a composite signal 64. Generally, the signal 40 isanalog or digital and, when the signal 40 is analog, the compositesignal 64 is digital, and, when the signal 40 is digital, the compositesignal 64 is analog.

The analysis and synthesis filters 44 a-n and 60 a-n can be in any of anumber of configurations provided that the filters pass only discrete,or at most only slightly overlapping, portions of the frequency domainof the signal 40. It is preferred that the frequency bands of thesubband signals overlap as little as possible. Preferably, no more thanabout 5% and more preferably no more than about 1% of the frequencybands of adjacent subband signals overlap.

The filters can be analog or digital depending on the type of signal 40or the processed signal segments 56 a-n. Examples of suitable analoganalysis and synthesis filters include a suitably configured bandpassfilter formed by one or more low pass filters, one or more high passfilters, a combination of band reject and low pass filters, acombination of band reject and high pass filters, or one or more bandreject filters. Digital analysis and synthesis filters are typicallydefined by software architecture that provides the desired filterresponse.

In a preferred configuration shown in FIG. 4, the signal 40 isdecomposed by the analysis filter bank 46 (which includes analog ordigital analysis filters H_(k)(z) 44 a-n) into subband signals which areeach sampled by a downsampler 64 a-n performing an M-fold decimation(i.e., taking every M^(th) sample), and the sampled subband signals arefurther sampled after signal processing by an up-sampler 68 a-n (and/orexpander (which fills in L−1 zeros in between each sample)) and thefurther sampled subband signals are combined by a synthesis filter bank62 (that includes analog or digital synthesis filters G_(k)(z) 60 a-n).The sampled subband signals, denoted by x₀(n), x₁(n), . . . x_(m−1)(n),are the outputs of the N-band analysis filter bank and the inputs to theN-band synthesis filter bank. As a result of decimation, the subbandsignals are 1/N the rate of the input rate of the signal 40.

Preferably, the analysis and synthesis filters are perfectreconstruction filters such that the composite signal 64 is a delayedversion of the signal 40 (i.e., y(n)=u(n−L) where y(n) is the compositesignal, u(n) is the signal, and L is time of delay). Using perfectreconstruction filters, the subband signals 48 a-n can be downsampledwithout any loss in fidelity of the output signal. This downsampling ispermissible because the subband signals are of narrow bandwidth and theconsequence of the downsampling is that any processing application 52a-n that is embedded in the subbands can run at significantly reducedrates.

As will be appreciated, a perfect reconstruction filter system can beformed by a number of different methods, including quadrature mirrorfilter techniques. A preferred technique for designing a filter bank isknown as a least squares multiple input multiple output filter designnotation. According to this technique, which is illustrated in FIG. 21,a rational transfer matrix defining one of the filter banks is known,i.e., either H(z) or G^(T)(z), along with a rational transfer matrixF(z) defining the ideal output of the filter banks. Assuming that H(z)and F(z) are the known rational transfer matrices, the unknown rationaltransfer matrix, G^(T)(z), is determined by the following equation:

G ^(T)(z)=[F(z)U ^(T)(z ⁻¹)]+H ₀ ⁻¹(z)

where

H(z)=H₀(z)U(z);[H₀(z) is the minimum phase equivalent of H(z)]

U(z)U^(T)(z⁻¹)=I; Paraunitary

[F(z)U^(T)(z⁻¹)]_(x): Causal part of F(z)U^(T)(z⁻¹)

As will be appreciated if G^(T)(z) were known and H(z) were unkown, thenthe equation would be solved for H(z) rather than G^(T)(z), and G^(T)(z)would be decomposed into the following:

G ^(T)(z)=G ₀ ^(T)(z)U(z)

where G₀ ^(T)(z) is the minimum phase equivalent of G^(T)(z).

In a preferred embodiment, the rational transfer matrices of theanalysis and/or synthesis filters are mathematically expressed in apolyphase filter representation. Exemplary equations defining thedecomposition of the signal 40 by the analysis filters 44 a-n includethe following:${H(z)} = {\sum\limits_{l = 0}^{M - 1}{z^{1}{E_{1}\left( z^{M} \right)}}}$

where

M is the number of subbands (which is the same as the number of analysisfilters in the analysis filter bank; l is the subband designation);${E_{1}\left( z^{M} \right)} = {\sum\limits_{n = {- \infty}}^{\infty}{{e_{1}(n)}z^{- n}}}$

 e _(l)(n)=h(Mn+1), 0≦l≦M−1

(known as a Type 1 polyphase filter representation) and${H(z)} = {\sum\limits_{l = 0}^{M - 1}\quad {z^{- {({M - 1 - 1})}}{R_{1}\left( z^{u} \right)}}}$

where

R ₁(z ^(M))=E _(M−1−1)(z)

(known as Type 2 polyphase filter representation). As will beappreciated, other techniques exist for expressing a rational transfermatrix defining a filter system including impluse response and filterdescription.

Noble identities can be used to losslessly move the decimators to theleft of the analysis filters and the L-fold up-sampler and/or expanderto the right of the synthesis filters. In this manner, the analysis andsynthesis filters operate on lower rate data, thereby realizingsignificant computational savings. The noble identities include:

Identity I: Decimation by M followed by filtering defined by themathematical function H(z) is equivalent to filtering by H(z^(M))followed by decimation by M (FIG. 5A).

Identity II: Filtering by G(z) followed by an upsampling by L isequivalent to upsampling by L followed by filtering by G(z^(L)) (FIG.5B).

By way of example, assume H(z) defines an order N finite impulseresponse (FIR) digital analysis filter with impulse response h(n), M=2,u(n) is the source signal and X(n) is the subband signal. Using the type1 polyphase representation above, H(z) is decomposed to yield thefollowing:

H(z)=H ₀(z ²)+H ₁(z ²)

Based on the foregoing, FIG. 6 is a polyphase representation basedimplementation of H(z) without noble identities and FIG. 7 is apolyphase representation-based implementation of the analysis filtersH(z) using noble identities to move the decimators ahead of the analysisfilters. In this configuration, H₀(z²) and H₁(z²) are FIR filters oforder n₀+1 and n₁+1, where N=n₀+n₁+1. H₀(z²) and H₁(z²) operate at halfthe rate as compared to H(z) and therefore have two units of time inwhich to perform all the necessary computations, and the components arecontinually active (i.e., there are no resting times). Accordingly,there is an M-fold reduction in the number of multiplications andadditions per unit of time when using both polyphase representation andthe noble identities to implement an M-fold decimation filter.

Subband signal processing can take a variety of forms. In one embodimentshown in FIG. 8 which depicts a receiver and antenna architecture, thesource signal 40 and subband signals 48 a-n are in analog form and aplurality of quantizers or analog-to-digital converters are used toconvert the subband signals 48 a-n to digital form before furtherprocessing 82 (e.g., correlation for encoded subband signals, subbandsignal digital beamforming in multiple antenna systems, etc.) and/orsynthesis of the digital subband signals 78 a-n is performed. As notedabove, the subband signals 48 a-n are preferably sampled by each of thedecimators or downsamplers 64 a-n at a rate of at least about twice thebandwidth of the corresponding subband signal 48 a-n to maintainfidelity. As shown in FIG. 9, each quantizer, or analog-to-digitalconverter, 74 a-n determines the digital word or representation 90 a-nthat corresponds to the bin 86 a-n having boundaries capturing theamplitude of the analog subband signal at that time and outputs thedigital word or representation that represents the selected quantizationlevel assigned to the respective bin. The digital subband signals 78 a-nare converted 94 a-n from radio frequency (RF) to base band frequencyand optionally subjected to further signal processing 60. The processedsubband signals 98 are formed into a digital composite signal 102 by thesynthesis filter bank 60.

To provide increased accuracy, noise rejecting quantizers can beutilized as the quantizers 74 a-n. As will be appreciated, a noiserejecting quantizer assigns more bits to the portions of the subbandsignal having less noise (and therefore more signal) and fewer bits tothe noisy portion. This selective assignment is accomplished byadaptively moving the bin boundaries so as to narrow the bin width(thereby increasing quantization fidelity. An example of a designequation for a Lloyd-Max noise rejecting quantizer is as follows:${t_{k} = {\frac{x_{k - 1} + x_{k}}{2} + \frac{{\delta^{2}\left( x_{k} \right)} - {\delta^{2}\left( x_{k - 1} \right)}}{2\left( {x_{k} - x_{k - 1}} \right)}}};{x_{k} = {e_{k} - {\frac{1}{2}\quad \frac{{\delta^{2}\left( x_{k} \right)}}{x_{k}}}}}$

where:

x is the signal to be quantized;

N is the number of quantization levels;

k is signal identifier;

σ is the noise covariance.

The mean squared quantization error (MSE) ξ² is as follows:$\xi^{2} = {\left( {E\left( {x - \hat{x}} \right)} \right)^{2} = {E_{x}^{2} + {\sum\limits_{k = 0}^{N - 1}{\left\lbrack {{\sigma^{2}\left( x_{k} \right)} + x_{k}^{2} - {2x_{k}e_{k}}} \right\rbrack P_{k}}}}}$

where:

{x_(k)}₀ ^(N−1) are the representation points;

{c_(k)}₀ ^(N−1) are the quantization bins;

{t_(k)}₀ ^(N−1) are the bin thresholds;

f_(y)(y) is the probability density function of y;

y=x+n, where x is the signal component and n the noise component;$\begin{matrix}{{e_{k} = {\left. {{Ex}{{y \in C_{k}}}} \right\rbrack = {{1/P_{k}}{\int_{t_{k}}^{t_{k + 1}}{{E\left\lbrack {{xy} = \alpha} \right\rbrack}{{fy}(\alpha)}{\alpha}}}}}};\quad {and}} \\{P_{k} = {{P\left\lbrack {y \in C_{k}} \right\rbrack} = {\int_{t_{k}}^{t_{k + 1}}{{{fy}(\alpha)}{\alpha}}}}}\end{matrix}$

The LM equations require that the bin thresholds be equidistant from therepresentation points and that each representation point be theconditional mean of x in the corresponding quantization bin. As will beappreciated, a Lloyd-Max (LM) quantizer substantially minimizes the meansquared error between the discrete approximation of the signal and itscontinuous representation.

The noise covariance, δ, can be estimated by linear mean squared errorestimation techniques. Linear mean squared error estimates arecharacterized by the following equation:

{circumflex over (X)}=Ty=R _(xy) R _(yy) ⁻¹ y

where T is the Wiener filter, R_(xy) is the cross covariance between xand y and R_(yy) is the covariance of y.

R_(xy) and R_(yy) are unknown and require estimation. A number oftechniques can be used to estimate R_(xy) and R_(yy), including anadaptive Wiener filter (e.g., using the linear mean squared algorithm),direct estimation, sample matrix inversion and a recursive, adaptiveWiener filter, with a recursive, adaptive Wiener filter being morepreferred.

The recursive, adaptive Wiener filter is explained in Thomas, J. K.,Canonical Correlations and Adaptive Subspace Filtering, Ph.DDissertation, University of Colorado Boulder, Department of Electricaland Compute Engineering, pp.1-110, June 1996. which is incorporatedherein by reference in its entirety. In a recursive, adaptive Wienerfilter assume {circumflex over (T)}_(M) denotes the filter when Mmeasurements of X and Y are used. Then {circumflex over (T)}_(M) is theadaptive Wiener filter

{circumflex over (T)} _(M) =X _(M) Y _(M)*(Y _(M) Y _(M)*)⁻¹={circumflex over (R)} _(xy) {circumflex over (R)} _(yy) ⁻¹,

X _(M) =[x ₁ x ₂ . . . x _(M) ]; X _(M+1) =[x _(M) x]

Y _(M) =[y ₁ y ₂ . . . y _(M) ]; Y _(M+1) =[y _(M) y]

If another measurement of x and y is taken, and one more column is addedto X_(M) and Y_(M) to build {circumflex over (T)}_(M+1):

{circumflex over (T)} _(M+1) =X _(M) Y _(M) *{circumflex over (R)}_(M+1) ⁻¹ +xy*{circumflex over (R)} _(M+1) ⁻¹

The estimate of _(M+1) is {circumflex over (X)}_(M+1)

{circumflex over (X)} _(M+1) ={circumflex over (T)} _(M+1) Y _(M+1)

Using the estimate of X_(M+1), one can read off {circumflex over(x)}_(M+1), which is the estimate of x:${\hat{x}}_{M + 1} = {{\frac{1}{1 + r^{2}}\quad {\overset{\sim}{x}}_{M}} + \frac{r^{2}}{1 + r^{2}}}$

where r²=y*{circumflex over (R)}_(M) ⁻¹y and {tilde over(x)}_(M+1)={circumflex over (T)}_(M)y.

Based on the above, when one observes y, the best estimate of theunknown x is {tilde over (x)}, with corresponding estimation error{tilde over (E)}_(M+1) and covariance {tilde over (Q)}_(M+1). If theunknown x becomes available after a delay, then {tilde over (x)}_(M+1)can be updated to {circumflex over (x)}_(M+1) with error covarianceÊ_(M+1) and covariance {tilde over (Q)}_(M+1). The two covariances arerelated by the following formula:${\overset{\sim}{Q}}_{M + 1} = {{\hat{Q}}_{M + 1} + {\frac{r^{2}}{1 + r^{2}}\quad {xx}^{*}}}$

By way of example and as illustrated in FIG. 19, consider a digitalcommunication application in which the modulation scheme involvestransmitting x₀ and x₁ when bits 0 and 1 are to be sent. During thesetup of the communication link, the transmitter sends a known bitsequence across the unknown channel. Let X_(M) be the matrix of signalsthat correspond to the known bit sequence. The receiver observes Y_(M),which is the channel filtered and noise corrupted version of X_(M).Since the receiver knows the bit pattern, and therefore X_(M), it isable to build {circumflex over (T)}_(M). Therefore we refer to X_(M) andY_(M) as the training set.

Once the communication link is established, the transmitter sends asignal x, which corresponds to a data bit. The receiver observes thecorresponding y and uses it to estimate x using {circumflex over(T)}_(M):

{tilde over (x)}={circumflex over (T)} _(M) y

The receiver determines r², cos²θ and sin²θ.

When cos²θ is approximately equal to 1, {tilde over (x)} is deemed to bea good estimate of x and is used to decide if a 1 or 0 was sent. If,however, cos²θ<<1, then the estimate {tilde over (x)} is scaled bycos²θ, as required by equation 14, before it is used to decide if a 1 or0 was sent. Once the decision of 1 or 0 is made, the true x is known andcan be used to build {circumflex over (x)} as required by equation 14above and as illustrated in FIG. 19. The x and y are also added to thetraining set to update {circumflex over (T)}_(M).

In another embodiment, the source signal 40 is digital and the analysisfilters are therefore digital, signal processing is performed by adigital-to-analog converter, and the synthesis filters are analog. FIG.10 depicts a subband digital transmitter according to this embodiment.The signal 100 is in digital format and is transmitted to a bank ofanalysis filters 104 a-n to form a plurality of digital subband signals108 a-n; the digital subband signals 108 a-n are processed bydigital-to-analog converters 112 a-n to form analog subband signals 116a-n; the analog subband signals 116 a-n are amplified by amplifiers 120a-n to form amplified subband signals 124 a-n; and the amplified subbandsignals 124 a-n transmitted via antennas 128 a-n.

In another embodiment shown in FIG. 11, a subband analog transmitter isdepicted where the signal 140 is analog and not digital. The signal 140is decomposed into a plurality of analog subband signals 144 a-n byanalog analysis filters 148 a-n and the analog subband signals 144 a-namplified by amplifiers 152 a-n, and the amplified subband signalstransmitted by antennas 156 a-n.

In yet another embodiment shown in FIG. 12, a subband receiver isdepicted that is compatible with the subband analog transmitter of FIG.11. Referring to FIG. 12, a plurality of subband signals 160 a-n arereceived by a plurality of antennas 164 a-n, the received subbandsignals 168 a-n down converted from radio frequency to basebandfrequency by down converters 172 a-n; the down converted subband signals176 a-n which are in analog form are converted by quantizers 180 a-nfrom analog to digital format; and the digital subband signals 184 a-ncombined by synthesis filters 188 a-n to form the digital compositesignal 192.

In any of the above-described transmitter or receiver embodiments, whenthe subband signals are encoded waveforms such as Code Division MultipleAccess (CDMA) or precision P(Y) GPS code signals, the subband signalscan be encoded or decoded to realize computational savings. In areceiver, for example, the subband signals are correlated with a replicaof the transmitted signal prior to detection. The correlation processcan be performed before or after synthesis filtering or beforeconversion to digital (and therefore in analog) or after conversion todigital (and therefore in digital). The approach is particularly usefulfor the rapid, direct acquisition of wideband pseudorandom noise encodedwaveforms, like CDMA type signals and the P(Y) GPS code, in a mannerthat is robust with respect to multipath effects and wide-band noise.Because the M-subband signals have narrow bandwidths and therefore canbe searched at slower rates, correlation of the subband signals ratherthan the signal or the composite signal can be performed with over anM-fold reduction in computation and therefore reduce the individualcomponent cost.

To provide further reductions in computational requirements, the numberof subbands requiring correlation at any trial time and Dopplerfrequency can be reduced. The pseudorandom nature of the coded signalsimplies that a coded signal will only lie in certain known subbands atany given time. According to the rank-reduction principle and asillustrated by FIG. 13, subbands 200 a-j outside of the subbands 204 a-jcontaining the coded signal can be eliminated to reduce the effects ofwide-band noise in the acquisition and/or tracking of pseudorandomsignals. This is accomplished by eliminating any subband in which thenoise component exceeds the signal component (i.e., the SNR is less than1). Such an elimination increases the bias squared, which is the powerof the signal components that are eliminated, while drasticallydecreasing the variance, which is the power of the noise that waseliminated. In this manner, the mean squared error between the computedcorrelation function and the noise-free version of the correlationfunction is significantly reduced.

As shown in FIG. 14 to perform the correlation in the subband signals inGPS, CDMA, and other pseudorandom or random waveform applications, thereplicated code 208 from the code generator 212 must be passed throughan analysis filter bank 216 that is identical to the analysis filterbank 220 used to decompose the signal 224. Because the correlation mustbe performed for different segments of the replicated code 208, eachindexed by some start time, this decomposition is necessary for alltrial segments of the replicated code 208. A plurality of subbandcorrelators 228 a-n receive both the subband signals 232 a-n and thereplicated subband signals 236 a-n and generate a plurality of subbandcorrelation signals 240 a-n. The subband correlation signals 240 a-n areprovided by the following equation:${q_{m,n}^{(i)}(j)} = {\sum\limits_{k = 1}^{N}{{X_{m}\left( {k + j} \right)}{p_{n}^{(i)}(k)}}}$

where:

q(k) is the subband correlation signal;

p_(n) ^((i))(k) is the component of the i^(th) trial segment of the P(Y)code in the n^(th) subband;

x_(m)(k) is the component of the measurement that lies in the m^(th)subband;

N is the number of samples over which the correlation is performed.

The subband correlation signals 240 a-n are upsampled and interpolatedby the synthesis filters 244 a-n and then squared and combined. Theresulting composite signal 248 is the correlation function that can befurther processed and detected.

After the subband correlation signals 240 a-n are generated, thesignals, for example, can be processed by a RAKE processor, which iscommonly a maximal SNR combiner, to align in both time and phasemultipath signals before detection and thereby provide improvedsignal-to-noise ratios and detection performance. As will beappreciated, a signal can be fragmented and arrive at a receiver viamultiple paths (i.e., multipath signals) due to reflections from otherobjects, particularly in urban areas. The formation of a number ofmultipath signals from a source signal can degrade the correlationpeaks, which contributes to the degradation of the detections. The RAKEprocessor determines the time and phase delays of these multipathsignals by searching for correlation peaks in the correlation functionand identifying the time and phase delays for each of the peaks. TheRAKE processor then uses the time and phase delay estimates to realignthe multipath signals so that they can add constructively and enhancethe correlation peaks. The peak enhancement improves detection becauseof the increase in signal-to-noise ratio.

FIG. 15 depicts an embodiment of a signal processing architectureincorporating these features. Referring to FIG. 11, the signals 300 arereceived by one or more antennas 304, down converted by a down converter308 to intermediate frequency, filtered by one or more filters 312, andpassed through an analog-to-digital converter 316 to form a digitalsignal 320. The digital signal 320 is passed through an analysis filterbank 324 to generate a plurality of subband signals 328 a-n, and thesubband signals 328 a-n to a plurality of subband correlators 332 a-n asnoted above to form a plurality of subband correlation signals 336 a-n.The subband correlation signals 336 a-n are passed to a synthesis filterbank 340 to form a correlation function 344 corresponding to the signal300. The correlation function 344 is passed to a pre-detector 348 todetermine an estimated transmit time and frequency and an amplitude anddelay for each of the correlation peaks. The estimated transmit time andfrequency 352 are provided to a code generator 356 and the amplitude andtime delay 360 associated with each correlation peak are provided to theRAKE processor 364. The code generator 356 determines a replicated code368 corresponding to the signal 300 based on the estimated trial timeand frequency. Using the correlation peak amplitudes and time and/orphase delays, the RAKE processor 364, as shown in FIG. 16, shifts theinput sequence y(k) by the amounts of the multipath time and/or phasedelays and then weights each shifted version by the amplitude of thepeak of the correlation function corresponding to that peak to form aRAKED signal 372 (denoted by y_(R)(k)). The RAKED sequence is commonlydefined by the following mathematical equation:${y_{R}(k)} = {\frac{1}{\sum\limits_{i = 1}^{p}A_{i}}{\sum\limits_{i = 1}^{p}{A_{i}^{{- {j\varphi}}\quad }{y\left( {k + t_{i}} \right)}}}}$

where:

p is the number of multipath signals (and therefore number of peaks);

A_(i) is the amplitude of the i^(th) peak;

t_(i) is the time delay of the i^(th) peak;

φ is the phase delay of the i^(th) peak;

y(k) is the input sequence into the code correlator. The RAKED signal372 and the replicated code 368 are correlated in a correlator 376 toprovide the actual transmit time and frequency 380 which are then usedby detector 384 to detect the signal.

There are a number of variations of the above-described system. Thevariations are useful in specific applications such as GPS, CDMA, andradar.

In one variation of the system of FIG. 15 that is depicted in FIGS.17-18, multiplexed radar transmitted receiver architectures aredepicted. The radar signals 400 a-n are a number of coded waveforms thatoperate in separate, contiguous subbands (referred to as “radar subbandsignals”). As shown in FIG. 17, the radar signals 40 are simultaneouslytransmitted by a plurality of transmitters 404 a-n that each include aplurality of analysis filters (not shown) to form the various radarsubband signals 400 a-n. Referring to FIG. 18, the various radar subbandsignals 400 a-n are received by a signal receptor 410 and passed througha plurality of bandpass filters 414 a-n. A bandpass filter 414 a-nhaving unique bandpass characteristics corresponds to each of the radarsubband signals. The various filtered subband signals 416 a-n aresampled by a plurality of decimators 422 a-n and quantized by aplurality of quantizers 426 a-n to form digital subband signals 430 a-n.The digital subband signals 430 a-n are analyzed by a plurality ofdetectors 434 a-n to form a corresponding plurality of detected signals438 a-n. The detectors 434 a-n use a differently coded waveform for eachof the transmitted radar subband signals 400 a-n so that the subbandradar signals can be individually separated upon reception. As notedabove in FIGS. 14-15, the coded radar waveform is decomposed by aplurality of analysis filters (not shown) that are identical to theanalysis filters in the receiver to provide replicated subband signalsto the detectors 434 a-n. Each detector 434 a-n correlates a radarsubband signal 430 a-n with its corresponding replicated subband signalto form a plurality of corresponding detected signals 438 a-n. Thedetected signals 438 a-n are analyzed by a synthesis filter bank 412 a-nto form a composite radar signal 446.

In a variation of the system of FIG. 15, a bank of analysis filters andsynthesis filters can be implemented both directly before and after thecorrelation step (not shown) to provide the above-noted reductions incomputational requirements.

In another variation of the system of FIG. 15, the analysis filters canbe relocated before the analog-to-digital converter 316 to form thesubband signals before as opposed to after conversion.

In another variation shown of the system of FIG. 15 that is depicted inFIG. 20, the RAKE processor 364 can account for the relative delays inantenna outputs of the signal 300 (which is a function of thearrangement of the antennas as well as the angular location of thesignal source) by summing the antenna outputs without compensating forthe relative output delays. The correlation process may result in N×ppeaks, where N is the number of antenna outputs and p is the number ofmultipath induced peaks. The Np peaks are then used to realign and scalethe input data before summation. The RAKE 364 in effect has performedthe phase-delay compensation usually done in beam-steering. Theadvantages of this approach compared to conventional beam steeringtechniques include that it is independent of antenna array geometriesand steering vectors, it does not require iterative searches fordirections as in LMS and its variants, and it is computationally veryefficient. This approach is discussed in detail in copending applicationhaving Ser. No. 08/916,884, and filed on Aug. 21, 1997.

While various embodiments of the present invention have been describedin detail, it is apparent that modifications and adaptations of thoseembodiments will occur to those skilled in the art. However, it is to beexpressly understood that such modifications and adaptations are withinthe scope of the present invention, as set forth in the followingclaims.

What is claimed is:
 1. A method for transmitting a signal, comprising:decomposing a signal having a signal bandwidth into at least first andsecond sub-band signals, each of the first and second sub-band signalshaving a respective sub-band signal bandwidth included within the signalbandwidth; transmitting each of the first and second sub-band signals;receiving each of the first and second sub-band signals; and combiningeach of the received first and second sub-band signals to form acomposite signal.
 2. The method of claim 1, wherein the transmittingstep comprises: encoding the first and second sub-band signals; andwherein the receiving step comprises: decoding the received first andsecond sub-band signals.
 3. The method of claim 2 wherein the first andsecond sub-band signals are encoded simultaneously and the receivedfirst and second sub-band signals are decoded simultaneously.
 4. Themethod of claim 1, wherein the decomposing step comprises: passing thesignal through an analysis filter, and wherein the combining stepcomprises: passing each of the first and second sub-band signals througha synthesis filter.
 5. The method of claim 1, wherein the transmittingstep comprises: emitting the at least first and second sub-band signalsfrom a corresponding plurality of signal sources; and wherein thereceiving step comprises: receiving the transmitted at least first andsecond sub-band signals with a corresponding plurality of signalreceptors.
 6. The method of claim 1, further comprising: converting thefirst and second sub-band signals from a digital form to an analog form.7. The method of claim 1, further comprising, before the combining step:converting the received first and second sub-band signals from a radiofrequency to a baseband frequency; and converting the baseband frequencyfirst and second sub-band signals from an analog format to a digitalformat.
 8. The method of claim 1, wherein the receiving step comprises:correlating the received first and second sub-band signals with areplica of the transmitted first and second sub-band signals.
 9. Themethod of claim 1, wherein the receiving step comprises: determiningwhether a respective noise component of the first and second sub-bandsignals is above a signal level; and when a noise component is above thesignal level, rejecting the corresponding sub-band signal.
 10. A systemfor transmitting a signal, comprising: means for decomposing a signalhaving a signal bandwidth into at least first and second sub-bandsignals, each of the first and second sub-band signals having arespective sub-band signal bandwidth included within the signalbandwidth; means for transmitting each of the first and second sub-bandsignals; means for receiving each of the first and second sub-bandsignals; and means for combining each of the received first and secondsub-band signals to form a composite signal.
 11. The system of claim 10,wherein the decomposing means comprises: an analysis filter and whereinthe combining means comprises a synthesis filter.
 12. The system ofclaim 11, wherein the analysis and synthesis filters are perfectreconstruction filters.
 13. The system of claim 10, wherein thetransmitting means comprises encoding means for encoding, prior totransmission, the first and second sub-band signals and wherein thereceiving means comprises decoding means for decoding the received firstand second sub-band signals.
 14. The system of claim 13 wherein thefirst and second sub-band signals are encoded simultaneously and thereceived first and second sub-band signals are decoded simultaneously.15. The system of claim 10, wherein the transmitting means comprises aplurality of signal sources corresponding to the at least a first andsecond sub-band signals and wherein the receiving means comprises aplurality of signal receptors corresponding to the received at leastfirst and second sub-band signals.
 16. The system of claim 10, furthercomprising: converting means for converting the first and secondsub-band signals from one of analog to digital or from digital toanalog.
 17. The system of claim 10, further comprising: down convertingmeans for converting the received first and second sub-band signals froma radio frequency to a baseband frequency; and analog-to-digitalconverting means for converting the baseband frequency first and secondsub-band signals from an analog format to a digital format.
 18. Thesystem of claim 10, wherein the receiving means comprises: correlatingmeans for correlating the received first and second sub-band signalswith a replica of the transmitted first and second sub-band signals. 19.The system of claim 10, wherein the receiving means comprises: means fordetermining whether a respective noise component of the first and secondsub-band signals is above a selected level; and means for rejecting atleast one of the first or second sub-band signal when the respectivenoise component is above the selected level.
 20. A system for signaltransmission, comprising: at least one analysis filter operable todecompose a signal having a signal bandwidth into at least first andsecond sub-band signals, each of the first and second sub-band signalshaving a respective sub-band signal bandwidth included within the signalbandwidth; and at least one transmitter operable to transmitindependently each of the first and second sub-band signals.
 21. Thesystem of claim 20, further comprising: at least one signal receptoroperable to receive each of the first and second sub-band signals; andat least one synthesis filter operable to combine each of the receivedfirst and second sub-band signals to form a composite signal.
 22. Thesystem of claim 21, further comprising: at least one encoder operable toencode, before transmission, the first and second sub-band signals; andat least one decoder operable to decode the received first and secondsub-band signals.
 23. The system of claim 22 wherein the first andsecond sub-band signals are encoded simultaneously and the receivedfirst and second sub-band signals are decoded simultaneously.
 24. Thesystem of claim 21, further comprising: a down converter operable toconvert the received first and second sub-band signals from a radiofrequency to a baseband frequency; and an analog-to-digital converteroperable to convert the baseband frequency first and second sub-bandsignals from an analog format to a digital format.
 25. The system ofclaim 21, further comprising: a correlator operable to correlate thereceived first and second sub-band signals with a replica of thetransmitted first and second sub-band signals.
 26. The system of claim21, further comprising: a noise reducing quantizer that, in a firstmode, is operable to determine whether a respective noise component ofthe first and second sub-band signals is above a signal level and, in asecond mode, is operable to reject the corresponding sub-band signalwhen a noise component is above the signal level.
 27. The system ofclaim 20, wherein the first and second sub-band signals are digital andfurther comprising: a digital-to-analog converter operable to convertthe first and second sub-band signals to an analog format.
 28. A methodfor transmitting a signal, comprising: decomposing a signal having asignal bandwidth into at least first and second sub-band signals, eachof the first and second sub-band signals having a respective sub-bandsignal bandwidth included within the signal bandwidth and transmittingseparately each of the first and second sub-band signals.
 29. The methodof claim 28, further comprising: receiving each of the first and secondsub-band signals; and combining each of the first and second sub-bandsignals to form a composite signal.
 30. The method of claim 29, whereinthe transmitting step comprises: encoding the first and second sub-bandsignals; and wherein the receiving step comprises: decoding the receivedfirst and second sub-band signals.
 31. The method of claim 30, whereinthe first and second sub-band signals are encoded simultaneously and thereceived first and second sub-band signals are decoded simultaneously.32. The method of claim 29, wherein the transmitting step comprises:emitting the at least a first and second sub-band signals from acorresponding plurality of signal sources; and wherein the receivingstep comprises: receiving the transmitted at least a first and secondsub-band signals with a corresponding plurality of signal receptors. 33.The method of claim 29, further comprising: converting the first andsecond sub-band signals from an analog format to a digital format. 34.The method of claim 29, further comprising, before the combining step:converting the received first and second sub-band signals from a radiofrequency to a baseband frequency; and converting the baseband frequencyfirst and second sub-band signals from an analog format to a digitalformat.
 35. The method of claim 29, wherein the receiving stepcomprises: determining whether a respective noise component of the firstand second sub-band signals is above a selected level; and when a noisecomponent is above the selected level, rejecting the correspondingsub-band signal.
 36. A method for receiving transmitted first and secondsub-band signals, the transmitted first and second sub-band signalshaving respective first and second sub-band signal bandwidths and beingcomponents of a signal having a signal bandwidth that includes the firstand second signal bandwidths, comprising: receiving independently eachof the first and second sub-band signals; and combining each of thefirst and second sub-band signals to form a composite signal.
 37. Themethod of claim 36, further comprising: decomposing the signal into thefirst and second sub-band signals; and transmitting the first and secondsub-band signals.
 38. The method of claim 37, wherein the decomposingstep comprises: passing the signal through an analysis filter; andwherein the combining step comprises: passing each of the first andsecond sub-band signals through a synthesis filter.
 39. The method ofclaim 37, wherein the transmitting step comprises: emitting the at leasta first and second sub-band signals from a corresponding plurality ofsignal sources; and wherein the receiving step comprises: receiving thetransmitted at least a first and second sub-band signals with acorresponding plurality of signal receptors.
 40. The method of claim 37,further comprising: converting the first and second sub-band signalsegments from digital to analog.
 41. The method of claim 37, furthercomprising, before the combining step: converting the received first andsecond sub-band signals from a radio frequency to a baseband frequency;and converting the baseband frequency first and second sub-band signalsfrom an analog format to a digital format.
 42. The method of claim 37,wherein the transmitting step comprises: encoding the first and secondsub-band signals; and wherein the receiving step comprises: decoding thereceived first and second sub-band signals.
 43. The method of claim 37wherein the first and second sub-band signals are encoded simultaneouslyand the received first and second sub-band signals are decodedsimultaneously.
 44. The method of claim 37, wherein the receiving stepcomprises: correlating the received first and second sub-band signalswith a replica of the transmitted first and second sub-band signals. 45.The method of claim 37, wherein the receiving step comprises:determining whether a respective noise component of the first and secondsub-band signals is above a selected level; and when a noise componentis above the selected level rejecting the corresponding sub-band signal.46. A system for receiving transmitted first and second sub-bandsignals, the transmitted first and second sub-band signals havingrespective first and second sub-band signal bandwidths and beingcomponents of a signal having a signal bandwidth that includes the firstand second signal bandwidths, comprising: at least one signal receptoroperable to receive separately each of the first and second sub-bandsignals; and at least one synthesis filter operable to combine each ofthe first and second sub-band signals to form a composite signal. 47.The method of claim 46, further comprising: at least one analysis filteroperable to decompose the signal into the first and second sub-bandsignals; and at least signal emitter operable to transmit the first andsecond sub-band signals.
 48. The system of claim 47, further comprising:a plurality of encoders operable to encode the first and second sub-bandsignals; and a plurality of decoders operable to decode the receivedfirst and second sub-band signals.
 49. The system of claim 48 whereinthe first and second sub-band signals are encoded simultaneously and thereceived first and second sub-band signals are decoded simultaneously.50. The system of claim 47, wherein the at least one signal emittercomprises a plurality of transmitters and the at least one signalreceptor comprises a plurality of antennas.
 51. The system of claim 47,further comprising: a plurality of digital-to-analog converters operableto convert the first and second sub-band signals from digital to analog.52. The system of claim 47, further comprising: a plurality of downconverters operable to convert the received first and second sub-bandsignals from a radio frequency to a baseband frequency; and a pluralityof analog-to-digital converters operable to convert the basebandfrequency first and second sub-band signals from an analog format to adigital format.
 53. The system of claim 47, further comprising: aplurality of correlators operable to correlate the received first andsecond sub-band signals with a replica of the transmitted first andsecond sub-band signals.
 54. The system of claim 47, further comprising:a noise reducing quantizer operable in a first mode to determine arespective noise component of a sub-band signal is above a selectedlevel and in a second mode to reject the sub-band signal when therespective noise component of the sub-band signal is above the selectedlevel.